what specific social, political and legal problems seem to be evident in Salem?

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This is a complex question for this short-answer forum. In varying degrees, the instigators of the witch trials are working to serve their own self-interest. Abigail begins the hysteria when she finds it a convenient way to deflect attention from her own sins, and further points the accusations at Elizabeth to scheme her way into Proctor's arms. Tituba, the first charged, is also the first to confess when she realizes that a confession will save her life. Parris at first rankles against the witchcraft talk because it would undermine his reputation in the town, and later opposes the execution of prominent community members because their death would lead to popular uprising. Even Giles Corey died in the way he did because it was in his own interest – by not pleading and dying under the weighted rocks, he ensured that his property would pass to his sons rather than to the state.

Salem is a tight-knit community where there is no such thing as private business. Individual activities like church attendance or book reading or keeping poppets become admissible evidence in court. Miller speculates that the community of Salem sought to keep itself together by casting out undesirable individuals, and in so doing created the atmosphere necessary for the witch hunts. The court itself was an extension of this principle, desperately in search of external validity – Danforth cannot possibly exonerate some when others have already perished for the same crime. But for the accused, it is only the individual that matters. In the end, Proctor is left with nothing but his name and reputation.